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Parameter optimization in decoy-state phase-matching quantum key distribution

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Abstract

The phase-matching quantum key distribution (PM-QKD) protocol has been widely researched since it was proposed. In this paper, the performance of asymmetric PM-QKD protocol is discussed and the efforts of statistical fluctuation and source error on asymmetric PM-QKD protocol are analyzed through numerical simulations. In the case of limited data sets, system parameters need to be optimized to increase the key rate. However, traditional exhaustive traversal or local search algorithms cannot meet the time requirement of real-time communication. With the development of machine learning, using machine learning for parameter optimization has been widely applied in various disciplines. This paper uses recurrent neural network (RNN) to predict the optimization parameters of asymmetric PM-QKD. The results show that RNN can quickly and accurately predict optimization parameters, which can provide a reference for future real-time QKD networks.

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Data Availability

All data generated and analyzed during this study is available from the corresponding author on reasonable request.

References

  1. Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. Theoret. Comput. Sci. 560, 7–11 (2014)

    MathSciNet  MATH  Google Scholar 

  2. Ekert, A.K.: Quantum cryptography based on bell’s theorem. Phys. Rev. Lett. 67(6), 661 (1991)

    ADS  MathSciNet  MATH  Google Scholar 

  3. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74(1), 145 (2002)

    ADS  MATH  Google Scholar 

  4. Mayers, D.: Unconditional security in quantum cryptography. J. ACM 48(3), 351–406 (2001)

    MathSciNet  MATH  Google Scholar 

  5. Huttner, B., Imoto, N., Gisin, N., Mor, T.: Quantum cryptography with coherent states. Phys. Rev. A 51(3), 1863 (1995)

    ADS  Google Scholar 

  6. Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dušek, M., Lütkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81(3), 1301 (2009)

    ADS  Google Scholar 

  7. Lo, H.-K., Curty, M., Tamaki, K.: Secure quantum key distribution. Nat. Photonics 8(8), 595–604 (2014)

    ADS  Google Scholar 

  8. Diamanti, E., Lo, H.-K., Qi, B., Yuan, Z.: Practical challenges in quantum key distribution. npj Quantum. Inf. 2(1), 1–12 (2016)

    Google Scholar 

  9. Brassard, G., Lütkenhaus, N., Mor, T., Sanders, B.C.: Limitations on practical quantum cryptography. Phys. Rev. Lett. 85(6), 1330 (2000)

    ADS  MATH  Google Scholar 

  10. Hwang, W.-Y.: Quantum key distribution with high loss: toward global secure communication. Phys. Rev. Lett. 91(5), 057901 (2003)

    ADS  Google Scholar 

  11. Lo, H.-K., Ma, X., Chen, K.: Decoy state quantum key distribution. Phys. Rev. Lett. 94, 230504 (2005)

    ADS  Google Scholar 

  12. Wang, X.-B.: Beating the photon-number-splitting attack in practical quantum cryptography. Phys. Rev. Lett. 94(23), 230503 (2005)

    ADS  Google Scholar 

  13. Acín, A., Brunner, N., Gisin, N., Massar, S., Pironio, S., Scarani, V.: Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007)

    ADS  Google Scholar 

  14. Bera, S., Gupta, S., Majumdar, A.S.: Device-independent quantum key distribution using random quantum states. Quantum Inf. Process. 22, 109 (2023)

    ADS  MathSciNet  MATH  Google Scholar 

  15. Lo, H.-K., Curty, M., Qi, B.: Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108(13), 130503 (2012)

    ADS  Google Scholar 

  16. Li, Y., Sun, Z., Li, P., Li, Z., Wang, J., Zhou, L., Ma, H.: Polarization and orbital angular momentum coupling for high-dimensional measurement-device-independent quantum key distribution protocol. Quantum Inf. Process. 22, 147 (2023)

    ADS  MathSciNet  MATH  Google Scholar 

  17. Li, Z., Wang, X., Chen, Z., Shen, T., Yu, S., Guo, H.: Impact of non-orthogonal measurement in bell detection on continuous-variable measurement-device-independent quantum key distribution. Quantum Inf. Process. 22, 236 (2023)

    ADS  MathSciNet  MATH  Google Scholar 

  18. Boyer, M., Kenigsberg, D., Mor, T.: Quantum key distribution with classical bob. Phys. Rev. Lett. 99, 140501 (2007)

    ADS  MathSciNet  MATH  Google Scholar 

  19. Du, Z., Yang, Y., Ning, T.: Security analysis for single-state circular mediated semi-quantum key distribution. Quantum Inf. Process. 22, 280 (2023)

    ADS  MathSciNet  MATH  Google Scholar 

  20. Lucamarini, M., Yuan, Z.L., Dynes, J.F., Shields, A.J.: Overcoming the rate-distance limit of quantum key distribution without quantum repeaters. Nature 557(7705), 400–403 (2018)

    ADS  Google Scholar 

  21. Ma, X., Zeng, P., Zhou, H.: Phase-matching quantum key distribution. Phys. Rev. X 8(3), 031043 (2018)

    Google Scholar 

  22. Li, W., Wang, L., Zhao, S.: Phase matching quantum key distribution based on single-photon entanglement. Sci. Rep. 9(1), 15466 (2019)

    ADS  Google Scholar 

  23. Wang, X.-B., Yu, Z.-W., Hu, X.-L.: Twin-field quantum key distribution with large misalignment error. Phys. Rev. A 98(6), 062323 (2018)

    ADS  Google Scholar 

  24. Yu, Z.-W., Hu, X.-L., Jiang, C., Xu, H., Wang, X.-B.: Sending-or-not-sending twin-field quantum key distribution in practice. Sci. Rep. 9(1), 3080 (2019)

    ADS  Google Scholar 

  25. Cui, C., Yin, Z.-Q., Wang, R., Chen, W., Wang, S., Guo, G.-C., Han, Z.-F.: Twin-field quantum key distribution without phase postselection. Phys. Rev. Appl. 11(3), 034053 (2019)

    ADS  Google Scholar 

  26. Wang, W., Xu, F., Lo, H.-K.: Asymmetric protocols for scalable high-rate measurement-device-independent quantum key distribution networks. Phys. Rev. X 9(4), 041012 (2019)

    Google Scholar 

  27. Liu, H., Wang, W., Wei, K., Fang, X.-T., Li, L., Liu, N.-L., Liang, H., Zhang, S.-J., Zhang, W., Li, H., et al.: Experimental demonstration of high-rate measurement-device-independent quantum key distribution over asymmetric channels. Phys. Rev. Lett. 122(16), 160501 (2019)

    ADS  Google Scholar 

  28. Liang, W., Xue, Q., Jiao, R.: The performance of three-intensity decoy-state measurement-device-independent quantum key distribution. Quantum Inf. Process. 19, 1–9 (2020)

    MathSciNet  MATH  Google Scholar 

  29. Grasselli, F., Navarrete, Á., Curty, M.: Asymmetric twin-field quantum key distribution. New J. Phys. 21(11), 113032 (2019)

    ADS  MathSciNet  Google Scholar 

  30. He, S.-F., Wang, Y., Li, J.-J., Bao, W.-S.: Asymmetric twin-field quantum key distribution with both statistical and intensity fluctuations. Commun. Theor. Phys. 72(6), 065103 (2020)

    ADS  MathSciNet  MATH  Google Scholar 

  31. Zhang, X.-X., Wang, Y., Jiang, M.-S., Zhou, C., Lu, Y.-F., Bao, W.-S.: Finite-key analysis of asymmetric phase-matching quantum key distribution with unstable sources. J. Opt. Soc. Am. B 38(3), 724–731 (2021)

    ADS  Google Scholar 

  32. Ma, X., Fung, C.-H.F., Razavi, M.: Statistical fluctuation analysis for measurement-device-independent quantum key distribution. Phys. Rev. A 86(5), 052305 (2012)

    ADS  Google Scholar 

  33. Mao, C.-C., Zhou, X.-Y., Zhu, J.-R., Zhang, C.-H., Zhang, C.-M., Wang, Q.: Improved statistical fluctuation analysis for measurement-device-independent quantum key distribution with four-intensity decoy-state method. Opt. Express 26(10), 13289–13300 (2018)

    ADS  Google Scholar 

  34. Xu, F., Xu, H., Lo, H.-K.: Protocol choice and parameter optimization in decoy-state measurement-device-independent quantum key distribution. Phys. Rev. A 89(5), 052333 (2014)

    ADS  Google Scholar 

  35. Ren, Z.-A., Chen, Y.-P., Liu, J.-Y., Ding, H.-J., Wang, Q.: Implementation of machine learning in quantum key distributions. IEEE Commun. Lett. 25(3), 940–944 (2020)

    Google Scholar 

  36. Dong, Q., Huang, G., Cui, W., Jiao, R.: Parameter optimization in satellite-based measurement-device-independent quantum key distribution. Quantum Sci. Technol. 7(1), 015014 (2021)

    ADS  Google Scholar 

  37. Lu, W., Huang, C., Hou, K., Shi, L., Zhao, H., Li, Z., Qiu, J.: Recurrent neural network approach to quantum signal: coherent state restoration for continuous-variable quantum key distribution. Quantum Inf. Process. 17, 109 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  38. Wang, W., Lo, H.-K.: Machine learning for optimal parameter prediction in quantum key distribution. Phys. Rev. A 100, 062334 (2019)

    ADS  Google Scholar 

  39. Schuster, M., Paliwal, K.K.: Bidirectional recurrent neural networks. IEEE Trans. Signal Process. 45(11), 2673–2681 (1997)

    ADS  Google Scholar 

  40. Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural Comput. 9(8), 1735–1780 (1997)

    Google Scholar 

  41. Nie, Y.-F., Zhang, C.-M.: Afterpulse analysis for reference-frame-independent quantum key distribution. Quantum Inf. Process. 21, 340 (2022)

    ADS  MathSciNet  MATH  Google Scholar 

  42. Wang, X.-B., Yang, L., Peng, C.-Z., Pan, J.-W.: Decoy-state quantum key distribution with both source errors and statistical fluctuations. New J. Phys. 11(7), 075006 (2009)

    ADS  Google Scholar 

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Acknowledgements

This work is supported by Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications) (IPOC2023ZT05), P. R. China

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Lu Wang, Qin Dong & Rongzhen Jiao

  2. State Key Laboratory of Information Photonics and Optical Communication, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Rongzhen Jiao

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  1. Lu Wang
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  2. Qin Dong
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  3. Rongzhen Jiao
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Correspondence to Rongzhen Jiao.

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Wang, L., Dong, Q. & Jiao, R. Parameter optimization in decoy-state phase-matching quantum key distribution. Quantum Inf Process 22, 373 (2023). https://doi.org/10.1007/s11128-023-04130-x

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